Math Problem Statement

(X²+6x+9)÷(x+3)

Solution

The given expression is:

(x2+6x+9)(x+3)\frac{(x^2 + 6x + 9)}{(x + 3)}

Now, let's simplify it:

  1. First, factor the numerator:

x2+6x+9=(x+3)(x+3)=(x+3)2x^2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)^2

  1. Now, rewrite the expression:

(x+3)2(x+3)\frac{(x + 3)^2}{(x + 3)}

  1. Since x+3x + 3 is common in both the numerator and denominator, cancel out one factor of x+3x + 3:

(x+3)(x + 3)

So, the simplified expression is:

x+3x + 3

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

  1. How do you factor quadratic expressions like x2+6x+9x^2 + 6x + 9?
  2. Can all quadratics be factored in a similar manner?
  3. What happens if x=3x = -3 in the original expression?
  4. How do you handle rational expressions with more complex numerators and denominators?
  5. What if the denominator had an additional factor?

Tip: Always check for factors in the numerator and denominator before simplifying expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Factoring Quadratics
Simplification of Rational Expressions

Formulas

Factoring a perfect square trinomial: (x + a)^2 = x^2 + 2ax + a^2

Theorems

Factorization Theorem
Cancellation Law in Rational Expressions

Suitable Grade Level

Grades 8-10